Reading Assignments - Math 104 - Calculus II
    March 1998

    I'll use Maple syntax for mathematical notation on this page.
    Be sure to check back often, because the assignments may change.

    For March 2

    Section 8.3 Arclength
    • To read: All
    • Be sure to understand: The statement of the Fact at the bottom of page 468, and Example 2. We'll talk about the section How Long is Cn? in class.

    Email Subject Line: Math 104 3/2 Your Name

    Reading Question:

      Use the Fact on page 468 to set up the integral that gives the length of the curve y=x3 from x=1 to x=3.

    For March 4

    Section 10.1 When Is an Integral Improper?
    • To read: All
    • Be sure to understand: Examples 1, 2, and 4. The formal definitions of convergence and divergence on pages 523 and 524.

    Email Subject Line: Math 104 3/4 Your Name

    Reading Questions:

    1. What are the two ways in which an integral may be improper?
    2. Explain why int( 1/x2, x=1..infty) is improper. Does the integral converge or diverge?
    3. Explain why int( 1/x2, x=0..1) is improper. Does the integral converge or diverge?

    For March 6

    Work on Project 2 today. No Reading Assignment.

    For March 9

    Section 10.2 Detecting Convergence, Estimating Limits
    • To read: Through Example 5
    • Be sure to understand: Example 2 and the statement of Theorem 1

    Email Subject Line: Math 104 3/9 Your Name

    Reading Questions:

    1. If 0 < f(x) < g(x) and int( g(x), x=1. . infty) converges, will int(f(x), x=1. .infty) converge or diverge? Why?
    2. There are two types of errors that arise in Example 2 for approximating int( 1/(x5 +1), x=1..infty). What are the two types?

    For March 11

    Section 10.2 Detecting Convergence, Estimating Limits (continued)
    • To read: The remainder of the section.
    • Be sure to understand: The statement of Theorem 2

    Email Subject Line: Math 104 3/11 Your Name

    Reading Questions: Suppose that 0 < f(x) < g(x).

    1. If int(f(x), x=1. .infty) diverges, what can you conclude about int( g(x), x=1. . infty)?
    2. If int(g(x), x=1. .infty) diverges, what can you conclude about int( f(x), x=1. . infty)?

    For March 13

    Section 10.4 l'Hopital's Rule: Comparing Rates
    • To read: All, but you may skip the section on Fine Print: Pointers Toward a Proof. We'll talk about a different justification during class.
    • Be sure to understand: The statement of Theorem 3, l'Hopital's Rule.

    Email Subject Line: Math 104 3/13 Your Name

    Reading Questions:

    1. Does l'Hopital's Rule apply to lim(x -> infty) x2 / ex ? Why or why not?
    2. Does l'Hopital's Rule apply to lim(x -> infty) x2 / sin(x) ? Why or why not?

    March 16 - 20

    Spring Break

    For March 23

    First day after Spring Break, so No Reading Assignment.

    For March 25

    Section 11.1 Sequences and Their Limits
    • To read: Through page 557 and the statements of Theorem 2 and Theorem 3.
    • Be sure to understand: The section of Fine Points on page 553, the statements of Theorems 2 and 3.

    Email Subject Line: Math 104 3/25 Your Name

    Reading Questions:

    1. Does the following sequence converge or diverge? Be sure to explain your answer.
      1, 3, 5, 7, 9, 11, 13, . . .
    2. Find a symbolic expression for the general term ak of the sequence
      1, -2, 4, -8, 16, -32, . . .

    For March 27

    Exam 2 today. No Reading Assignment.

    For March 30

    Section 11.2 Infinite Series, Convergence, and Divergence

    • To read: Through Example 4. This can be tough going.
    • Be sure to understand: The section Series Language: Terms, Partial Sums, Tails, Convergence, Limit on page 563

    Email Subject Line: Math 104 3/30 Your Name

    Reading Questions:

    1. There are two sequences associated with every series. What are they?
    2. Does the geometric series Sigma (1/2)k converge or diverge?

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